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Product Rule

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Wize University Calculus 1 Textbook > Derivatives

The Product Rule

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Suppose g(x)g\left(x\right) is differentiable, f(x)=x2g(x)f\left(x\right)=x^2g\left(x\right). Given that f′(3)=30f'\left(3\right)=30, f′′(3)=19f''\left(3\right)=19, g(3)=2g\left(3\right)=2, what is g′(3)g'\left(3\right) and g′′(3)g''\left(3\right)?
More The Product Rule Questions:
Product Rule
Suppose g(x)g\left(x\right) is differentiable, f(x)=x2g(x)f\left(x\right)=x^2g\left(x\right). Given that f′(3)=30f'\left(3\right)=30, f′′(3)=19f''\left(3\right)=19, g(3)=2g\left(3\right)=2, what is g′(3)g'\left(3\right) and g′′(3)g''\left(3\right)?
Product Rule
Suppose g(x)g\left(x\right) is differentiable, f(x)=x2g(x)f\left(x\right)=x^2g\left(x\right). Given that f′(3)=30f'\left(3\right)=30, f′′(3)=19f''\left(3\right)=19, g(3)=2g\left(3\right)=2, what is g′(3)g'\left(3\right) and g′′(3)g''\left(3\right)?
Product Rule
Suppose g(x)g\left(x\right) is differentiable, f(x)=x2g(x)f\left(x\right)=x^2g\left(x\right). Given that f′(3)=30f'\left(3\right)=30, f′′(3)=19f''\left(3\right)=19, g(3)=2g\left(3\right)=2, what is g′(3)g'\left(3\right) and g′′(3)g''\left(3\right)?
Product Rule
Suppose g(x)g\left(x\right) is differentiable, f(x)=x2g(x)f\left(x\right)=x^2g\left(x\right). Given that f′(3)=30f'\left(3\right)=30, f′′(3)=19f''\left(3\right)=19, g(3)=2g\left(3\right)=2, what is g′(3)g'\left(3\right) and g′′(3)g''\left(3\right)?
Product Rule
Suppose g(x)g\left(x\right) is differentiable, f(x)=x2g(x)f\left(x\right)=x^2g\left(x\right). Given that f′(3)=30f'\left(3\right)=30, f′′(3)=19f''\left(3\right)=19, g(3)=2g\left(3\right)=2, what is g′(3)g'\left(3\right) and g′′(3)g''\left(3\right)?
Product Rule
Suppose g(x)g\left(x\right) is differentiable, f(x)=x2g(x)f\left(x\right)=x^2g\left(x\right). Given that f′(3)=30f'\left(3\right)=30, f′′(3)=19f''\left(3\right)=19, g(3)=2g\left(3\right)=2, what is g′(3)g'\left(3\right) and g′′(3)g''\left(3\right)?
Product Rule
Suppose g(x)g\left(x\right) is differentiable, f(x)=x2g(x)f\left(x\right)=x^2g\left(x\right). Given that f′(3)=30f'\left(3\right)=30, f′′(3)=19f''\left(3\right)=19, g(3)=2g\left(3\right)=2, what is g′(3)g'\left(3\right) and g′′(3)g''\left(3\right)?
Product Rule
Suppose g(x)g\left(x\right) is differentiable, f(x)=x2g(x)f\left(x\right)=x^2g\left(x\right). Given that f′(3)=30f'\left(3\right)=30, f′′(3)=19f''\left(3\right)=19, g(3)=2g\left(3\right)=2, what is g′(3)g'\left(3\right) and g′′(3)g''\left(3\right)?
Product Rule
Suppose g(x)g\left(x\right) is differentiable, f(x)=x2g(x)f\left(x\right)=x^2g\left(x\right). Given that f′(3)=30f'\left(3\right)=30, f′′(3)=19f''\left(3\right)=19, g(3)=2g\left(3\right)=2, what is g′(3)g'\left(3\right) and g′′(3)g''\left(3\right)?
Product Rule
Suppose g(x)g\left(x\right) is differentiable, f(x)=x2g(x)f\left(x\right)=x^2g\left(x\right). Given that f′(3)=30f'\left(3\right)=30, f′′(3)=19f''\left(3\right)=19, g(3)=2g\left(3\right)=2, what is g′(3)g'\left(3\right) and g′′(3)g''\left(3\right)?
Product Rule
Suppose g(x)g\left(x\right) is differentiable, f(x)=x2g(x)f\left(x\right)=x^2g\left(x\right). Given that f′(3)=30f'\left(3\right)=30, f′′(3)=19f''\left(3\right)=19, g(3)=2g\left(3\right)=2, what is g′(3)g'\left(3\right) and g′′(3)g''\left(3\right)?
Product Rule
Suppose g(x)g\left(x\right) is differentiable, f(x)=x2g(x)f\left(x\right)=x^2g\left(x\right). Given that f′(3)=30f'\left(3\right)=30, f′′(3)=19f''\left(3\right)=19, g(3)=2g\left(3\right)=2, what is g′(3)g'\left(3\right) and g′′(3)g''\left(3\right)?
Product Rule
Suppose g(x)g\left(x\right) is differentiable, f(x)=x2g(x)f\left(x\right)=x^2g\left(x\right). Given that f′(3)=30f'\left(3\right)=30, f′′(3)=19f''\left(3\right)=19, g(3)=2g\left(3\right)=2, what is g′(3)g'\left(3\right) and g′′(3)g''\left(3\right)?
Product Rule
Suppose g(x)g\left(x\right) is differentiable, f(x)=x2g(x)f\left(x\right)=x^2g\left(x\right). Given that f′(3)=30f'\left(3\right)=30, f′′(3)=19f''\left(3\right)=19, g(3)=2g\left(3\right)=2, what is g′(3)g'\left(3\right) and g′′(3)g''\left(3\right)?
Product Rule
Q:\textbf{Q:} Differentiate f(x)=(x3/2)(2x4−5x2−x−1)(xe−π3.5)\displaystyle f(x)=(x^{3/2})\left(2x^{4}-5x^{2}-x^{-1}\right)(x^{e}-\pi^{3.5})
Quotient and Product
Find the derivative of g(t)=(1+2t7t)(t2−1)\displaystyle g(t)=\left(\frac{1+2t}{7t}\right)(t^{2}-1)
The product rule
Find the derivative of f(x)=x3exf(x) = x^3 e^x
The graph of w(x) is given below.
Practice: Product Rule*
Suppose g(x)g\left(x\right) is differentiable, f(x)=x2g(x)f\left(x\right)=x^2g\left(x\right). Given that f′(3)=30f'\left(3\right)=30, f′′(3)=19f''\left(3\right)=19, g(3)=2g\left(3\right)=2, what is g′(3)g'\left(3\right) and g′′(3)g''\left(3\right)?
Product Rule
Differentiate f(x)=(x3/2)(2x4−5x2−x−1)(xe−π3.5)\displaystyle f(x)=(x^{3/2})\left(2x^{4}-5x^{2}-x^{-1}\right)(x^{e}-\pi^{3.5})
Quotient and Product
Find the derivative of g(t)=(1+2t7t)(t2−1)\displaystyle g(t)=\left(\frac{1+2t}{7t}\right)(t^{2}-1)
Find the derivative of f(x)=(x3/2+2x)(x7/4+x)\displaystyle f(x)=\left(x^{3/2}+\frac{2}{x}\right)\left(x^{7/4}+x\right) .
Product Rule
Suppose g(x)g\left(x\right) is differentiable, f(x)=x2g(x)f\left(x\right)=x^2g\left(x\right). Given that f′(3)=30f'\left(3\right)=30, f′′(3)=19f''\left(3\right)=19, g(3)=2g\left(3\right)=2, what is g′(3)g'\left(3\right) and g′′(3)g''\left(3\right)?